The effects of unbalance on oil whirl

Abstract

Abstract. The nonlinear behavior of an unbalanced rotor supported in a fluid film bearing is analyzed. A simplified two dimensional model is adopted which uses the long-bearing approximation with a rr-tilm to account for cavitation. This model has been thoroughly studied by Myers I11 in the balanced case, where it is shown that the whirl instability is the result of a Hopf bifurcation. The implications of imbalance are studied in this paper. This leads to the study of a periodically perturbed Hopf bifurcation. It is shown that the dwaamics in this situation can. espcciall 3 under certain nonlinear resonance conditions, have an extremely complicated dependence on the system parameters and the rotor speed. Complete bifurcation diagrams are presented for a particular rotor model which demonstrate this dependence.

Dynamics and stability of turbocharger rotors

“…Remark: Before the rotor reaches the oil whirl region (complete instability at t ≈ 5,500 ms), self-excited oscillations with small amplitudes and a whirl frequency of ≈ 0.5ω Rotor are observed (see plot for ε at t ≈ 4,300 ms) [1][2][3][4].…”

“…[1]) with bearing eccentricities close to 1 (if external damping is small) may be rather sophisticated and depends on various system parameters, initial conditions, etc. [1][2][3][4]. Stable limit cycle oscillations with bearing eccentricities well below 1 -even for the case without external damping-may exist below and above the threshold of instability (see, e.g., Fig.…”

“…This work was extended to the unbalanced rotor in Ref. [2]. Bifurcations occurring in perfectly balanced rigid rotors supported in full-floating ring bearings are analyzed in Ref.…”

“…Subsynchronous). The analysis of such a bifurcation is difficult and sophisticated stability methods have to be applied [1][2][3][4]10,11,[19][20][21][22]. Note that application of the Floquet theorem is not possible, since the frequencies of the Synchronous and the 1.…”

Local and global bifurcations of valve mechanism

“…In recent ten years there have been some researchers who utilized theory of normal form and universal unfolding to study degenerate bifurcations of codimension two and global bifurcations of nonlinear oscillators, for example Holmes [5], Guckenheimer and Holmes [6], Bajaj [7,8], Shaw [9], Sri Namachchivaya [10], and Zhang et al [11,12]. Sri Namachchivaya et al [13] used averaging method and normal form theory to study in detail the effect of small periodic parametric excitation on a more general system.…”